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      Effects of homeostatic constraints on associative memory storage and synaptic connectivity of cortical circuits

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          The impact of learning and long-term memory storage on synaptic connectivity is not completely understood. In this study, we examine the effects of associative learning on synaptic connectivity in adult cortical circuits by hypothesizing that these circuits function in a steady-state, in which the memory capacity of a circuit is maximal and learning must be accompanied by forgetting. Steady-state circuits should be characterized by unique connectivity features. To uncover such features we developed a biologically constrained, exactly solvable model of associative memory storage. The model is applicable to networks of multiple excitatory and inhibitory neuron classes and can account for homeostatic constraints on the number and the overall weight of functional connections received by each neuron. The results show that in spite of a large number of neuron classes, functional connections between potentially connected cells are realized with less than 50% probability if the presynaptic cell is excitatory and generally a much greater probability if it is inhibitory. We also find that constraining the overall weight of presynaptic connections leads to Gaussian connection weight distributions that are truncated at zero. In contrast, constraining the total number of functional presynaptic connections leads to non-Gaussian distributions, in which weak connections are absent. These theoretical predictions are compared with a large dataset of published experimental studies reporting amplitudes of unitary postsynaptic potentials and probabilities of connections between various classes of excitatory and inhibitory neurons in the cerebellum, neocortex, and hippocampus.

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          Most cited references 89

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          Neural networks and physical systems with emergent collective computational abilities.

           John Hopfield (1982)
          Computational properties of use of biological organisms or to the construction of computers can emerge as collective properties of systems having a large number of simple equivalent components (or neurons). The physical meaning of content-addressable memory is described by an appropriate phase space flow of the state of a system. A model of such a system is given, based on aspects of neurobiology but readily adapted to integrated circuits. The collective properties of this model produce a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size. The algorithm for the time evolution of the state of the system is based on asynchronous parallel processing. Additional emergent collective properties include some capacity for generalization, familiarity recognition, categorization, error correction, and time sequence retention. The collective properties are only weakly sensitive to details of the modeling or the failure of individual devices.
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            Solvable Model of a Spin-Glass

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              Theory of spin glasses


                Author and article information

                Front Comput Neurosci
                Front Comput Neurosci
                Front. Comput. Neurosci.
                Frontiers in Computational Neuroscience
                Frontiers Media S.A.
                18 June 2015
                : 9
                Department of Physics and Center for Interdisciplinary Research on Complex Systems, Northeastern University Boston, MA, USA
                Author notes

                Edited by: Hava T. Siegelmann, Rutgers University, USA

                Reviewed by: Paul Miller, Brandeis University, USA; Mikhail Katkov, Weizmann Institute of Science, Israel

                *Correspondence: Armen Stepanyants, Department of Physics, Northeastern University, 110 Forsyth St., Boston, MA 02115, USA a.stepanyants@
                Copyright © 2015 Chapeton, Gala and Stepanyants.

                This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

                Page count
                Figures: 5, Tables: 0, Equations: 10, References: 91, Pages: 14, Words: 11026
                Funded by: NIH
                Award ID: R01NS063494
                Original Research


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